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A functional quantum programming language
 In: Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
, 2005
"... This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are inte ..."
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Cited by 57 (12 self)
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This thesis introduces the language QML, a functional language for quantum computations on finite types. QML exhibits quantum data and control structures, and integrates reversible and irreversible quantum computations. The design of QML is guided by the categorical semantics: QML programs are interpreted by morphisms in the category FQC of finite quantum computations, which provides a constructive operational semantics of irreversible quantum computations, realisable as quantum circuits. The quantum circuit model is also given a formal categorical definition via the category FQC. QML integrates reversible and irreversible quantum computations in one language, using first order strict linear logic to make weakenings, which may lead to the collapse of the quantum wavefunction, explicit. Strict programs are free from measurement, and hence preserve superpositions and entanglement. A denotational semantics of QML programs is presented, which maps QML terms
Quantum Programming Languages  Survey and Bibliography
 UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2006
"... The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechan ..."
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Cited by 35 (2 self)
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The field of quantum programming languages is developing rapidly and there is a surprisingly large literature. Research in this area includes the design of programming languages for quantum computing, the application of established semantic and logical techniques to the foundations of quantum mechanics, and the design of compilers for quantum programming languages. This article justifies the study of quantum programming languages, presents the basics of quantum computing, surveys the literature in quantum programming languages, and indicates directions for future research.
QML: Quantum data and control
, 2005
"... We introduce the language QML, a functional language for quantum computations on finite types. QML introduces quantum data and control structures, and integrates reversible and irreversible quantum computation. QML is based on strict linear logic, hence weakenings, which may lead to decoherence, hav ..."
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Cited by 6 (1 self)
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We introduce the language QML, a functional language for quantum computations on finite types. QML introduces quantum data and control structures, and integrates reversible and irreversible quantum computation. QML is based on strict linear logic, hence weakenings, which may lead to decoherence, have to be explicit. We present an operational semantics of QML programs using quantum circuits, and a denotational semantics using superoperators.
THE PHYSICAL CHURCHTURING THESIS AND THE PRINCIPLES OF QUANTUM THEORY
, 2012
"... As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is ..."
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Cited by 5 (2 self)
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As was emphasized by Deutsch, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet Nielsen and others have shown how quantum theory as it stands could breach the physical ChurchTuring thesis. We draw a clear line as to when this is the case, in a way that is inspired by Gandy. Gandy formulates postulates about physics, such as homogeneity of space and time, bounded density and velocity of information — and proves that the physical ChurchTuring thesis is a consequence of these postulates. We provide a quantum version of the theorem. Thus this approach exhibits a formal nontrivial interplay between theoretical physics symmetries and computability assumptions.
Quantum Programming Languages: An Introductory Overview
, 2006
"... The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area ..."
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Cited by 4 (0 self)
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The present article gives an introductory overview of the novel field of quantum programming languages (QPLs) from a pragmatic perspective. First, after a short summary of basic notations of quantum mechanics, some of the goals and design issues are surveyed, which motivate the research in this area. Then, several of the approaches are described in more detail. The article concludes with a brief survey of current research activities and a tabular summary of a selection of QPLs, which have been published so far.
Around the physical ChurchTuring thesis: Cellular automata, formal languages, and the principles of quantum theory
 In Proc. 6th International Conference on Language and Automata Theory and Applications (LATA 2012, A Coruña
, 2012
"... Abstract. The physical ChurchTuring thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density ..."
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Abstract. The physical ChurchTuring thesis explains the Galileo thesis, but also suggests an evolution of the language used to describe nature. It can be proved from more basic principle of physics, but it also questions these principles, putting the emphasis on the principle of a bounded density of information. This principle itself questions our formulation of quantum theory, in particular the choice of a field for the scalars and the origin of the infinite dimension of the vector spaces used as state spaces1. 1 The ChurchTuring Thesis and Its Various Forms 1.1 Why a Thesis? It is a quite common situation in mathematics, that a notion, first understood intuitively, receives a formal definition at some point. For instance, the notion of a real number has been understood intuitively in geometry, for instance as the length of a segment, before it has been formally defined in the 19th century, by Cauchy and Dedekind. Another example is the notion of an algorithm, that has been understood intuitively for long, before a formal definition of the notion of a
Programming with Quantum Communication
"... Abstract. We present a formal framework for specifying, implementing, and analysing quantum communication protocols. 1 ..."
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Abstract. We present a formal framework for specifying, implementing, and analysing quantum communication protocols. 1
Programming Telepathy: Implementing Quantum Nonlocality Games
 SBMF 2008
, 2008
"... Quantum pseudotelepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum nonlocality games. The setting o ..."
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Quantum pseudotelepathy is an intriguing phenomenon which results from the application of quantum information theory to communication complexity. To demonstrate this phenomenon researchers in the field of quantum communication complexity devised a number of quantum nonlocality games. The setting of these games is as follows: the players are separated so that no communication between them is possible and are given a certain computational task. When the players have access to a quantum resource called entanglement, they can accomplish the task: something that is impossible in a classical setting. To an observer who is unfamiliar with the laws of quantum mechanics it seems that the players employ some sort of telepathy; that is, they somehow exchange information without sharing a communication channel. This paper provides a formal framework for specifying, implementing, and analysing quantum nonlocality games.
Under consideration for publication in Math. Struct. in Comp. Science Relations among Quantum Processes:
, 2005
"... Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, ..."
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Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components, as well as communications between these components. Moreover, to model concurrent and distributed quantum computations and quantum communication protocols, communications over quantum channels which move qubits physically from one place to another must also be taken into account. Inspired by classical process algebras, which provide a framework for modeling cooperating computations, a process algebraic notation is defined. This notation provides a homogeneous style to formal descriptions of concurrent and distributed computations comprising both quantum and classical parts. Based upon an operational semantics which makes sure that quantum objects, operations and communications operate according to the postulates of quantum mechanics, an equivalence is defined among process states considered as having the same behavior. This equivalence is a probabilistic branching bisimulation. From this relation, an equivalence on processes is defined. However, it is not a congruence because it is not preserved by parallel composition. 1.